First slide

Conduction

Question

One end of a cylindrical rod is kept in steam chamber and the other end in melting Ice. Now 0.5 gm of ice melts in 1 sec. If the rod is replaced by another rod of same length, half the diameter and double the conductivity of the first rod, then rate of melting of ice will be

Moderate

A

0.25 gm/sec
B

0.5 gm/sec
C

1 gm/sec
D

2 gm/sec

Solution

$\large \frac Qt=\frac {kA\Delta \theta}{l}\Rightarrow \frac {mL}{t}=\frac {kA\Delta \theta}{l}$
$\large \[\frac{m}{t} \propto kA \Rightarrow \frac{m}{t} \propto k{r^2}\]$
$\large \frac {\left ( \frac mt \right )_1}{(\frac mt)_2}=\frac {k_1}{k_2}\left ( \frac {r_1}{r_2} \right )^2=\frac {k}{2k}\frac {r^2}{\left ( \frac {r^2}{4} \right )}$
$\large \left ( \frac mt \right )_2=0.25gm/sec$

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